Question

if sec θ+tan θ=p,prove that
sin θ=p²-1/ p²+1.

Answer 1

Given:- secθ + tanθ = p........(1)

Sol:- sec²θ - tan²θ = 1

⇒(secθ-tanθ)(secθ+tanθ) = 1

⇒p(secθ-tanθ) = 1

⇒secθ-tanθ = 1/p.......(2)

∴(1)+(2) ⇒ secθ + tanθ + secθ - tanθ = p + 1/p

⇒2secθ = p²+1/p

⇒secθ = p²+1/2p

∴cosθ = 2p/p²+1 (∵cosθ = 1/sinθ)

∴(1)-(2) ⇒ secθ + tanθ - secθ + tanθ = p - 1/p

⇒2tanθ = p-1/p

⇒tanθ = p²-1/2p

∴sinθ = cosθ . tanθ

⇒sinθ = 2p/p²+1 . p²-1/2p

⇒sinθ = p²-1/p²+1 ∴Hence Proved

Answer 2

Hey dear friend,

perfectly fine pure correct answer
hope it helps you mark me as brainliest and follow me